Question

A block slides down an inclined plane making an angle $\theta =30^{\circ}$ with the horizontal with an acceleration $\frac{g}{4}$ , then coefficient of frictions will be

• A. $\frac{1}{4}\left( \frac{\sqrt{3}}{2} \right)$
• B. $\frac{1}{4}-\frac{\sqrt{3}}{2}$
• C. $\frac{1}{2\sqrt{3}}$
• D. $2\sqrt{3}$

Answer 1

Answer: (C)

$\frac{1}{2\sqrt{3}}$

Answer 2

Acceleration is given by as $a=g \sin \theta-\mu g \cos \theta$ or $\frac{g}{4}=g(\sin \theta-\mu \cos \theta)$ or $\frac{1}{4}=\left(\sin 30^{\circ}-\mu \cos 30^{\circ}\right)$ or $\frac{1}{4}=\frac{1}{2}-\frac{\mu \sqrt{3}}{2}$ or $\frac{\mu \sqrt{3}}{2}=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$. $\mu=\frac{1}{2 \sqrt{3}}$